Method and device for ascertaining the steering angle of a steerable machine

ABSTRACT

The present invention relates to a device and method for ascertaining the steering angle (α 3 ) of at least one steerable wheel of a set of steerable wheels of a machine that can be directionally controlled, which machine comprises at least said set of steerable wheels and at least one set of drivable wheels showing a specific wheelbase (a 1 ) relative to said steerable wheels and spaced from one another by a specific track width (b 1 ), wherein by means of an ascertained wheel velocity difference of the two driven wheels a yaw rate (ψ) and a real circle radius (r 1 ) of the driven wheel on the inside of the curve are ascertained. It is then possible to ascertain the steering angle (α) from these values by way of the geometrical relationship of wheelbase (a 1 ) and track width (b 1 ) of the machine.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application claims priority under 35 U.S.C. §119 of GermanPatent Application Nos. 10 2012 025 457.1, filed Dec. 28, 2012 and 102013 005 991.7, filed Apr. 8, 2013, the disclosures of which are herebyincorporated herein by reference in their entireties.

FIELD OF THE INVENTION

The present invention relates to a method and device for ascertainingthe steering angle of at least one steerable wheel of a set of steerablewheels of a machine that can be directionally controlled, which machinecomprises at least said set of steerable wheels and at least one set ofdrivable wheels having a specific wheelbase a₁ relative to the steerablewheels, and a track width b₁ between the drivable wheels.

BACKGROUND OF THE INVENTION

In the prior art, self-propelled machines that can be steered, ordirectionally controlled, more particularly, construction machines thatare driven slowly, are controlled depending on the current steeringangle of a set of steerable wheels.

It is known, for instance, to apply remote directional control to such amachine with the aid of appropriate navigational equipment and totransmit steering commands thereto, depending on the position of themachine and the required work route. Such control can only workprecisely when the steering angles of the relevant steerable wheels usedfor directional control are known.

In this context, it is common practice to ascertain the steering anglesduring operation. Appropriate steering angle sensors can be, forexample, potentiometers adapted to send different signals to a controlor monitoring unit depending on the steering angle of the respectivewheel.

It has been found that such steering angle sensors suffer from thedrawback that they have a high tendency to failure. It has further beenfound that the results given by such steering angle sensors are notalways unequivocal to a satisfactory degree.

It is thus an object of the present invention to provide a device andmethod for determining the steering angle of a steerable wheel of a setof steerable wheels of a machine that can be directionally controlled asdescribed above, that make it possible to ascertain the steering angleof such a machine in a precise, inexpensive, and reliable manner.

SUMMARY OF THE INVENTION

In particular, this object is thus achieved by a method for ascertainingthe steering angle α₃ of at least one steerable wheel of a set ofsteerable wheels of a machine that can be directionally controlled,which machine comprises at least said set of steerable wheels and atleast one set of drivable wheels, which drivable wheels have a wheelbasea₁ relative to the steerable wheels, and a track width b₁ disposedtherebetween. This method comprises the following method steps:

-   -   detecting the wheel velocity of at least two drivable wheels;    -   ascertaining a wheel velocity difference Δv between the        velocities v₁, v₂ of the two wheels;    -   ascertaining the yaw rate (ψ) using the relationship

$\psi = \frac{v_{2} - v_{1}}{b_{1}}$

-   -   ascertaining the real circle radius r₁ of the drivable wheel on        the inside of the curve using the relationship

$r_{1} = \frac{v_{1}}{\psi}$

-   -   ascertaining the steering angle α₃ using the relationship

${\alpha_{3} = {{arc}\; {\tan \left( \frac{a_{1}}{r_{1}} \right)}}},$

-   -    wherein v₁ denotes the velocity of the drivable wheel on the        inside of the curve, v₂ the velocity of the drivable wheel on        the outside of the curve, ψ the yaw rate, α₃ the steering angle        of the steering wheel on the inside of the curve, r₁ the circle        radius of the drivable wheel on the inside of the curve, r₂ the        circle radius of the drivable wheel on the outside of the curve,        a₁ the wheelbase, and b₁ the track width.

This object is further achieved by a method comprising the followingmethod steps:

-   -   detecting the velocities (v₁, v₂), or values that are directly        related thereto, which values, unlike the vehicle-specific        constants, are ones that are constantly measured, for example,        the revolution counts n₁, n₂ of at least two wheels of the set        of drivable wheels;    -   ascertaining the real circle radius r₁ of the drivable wheel on        the inside of the curve using the relationship

${r_{1} = {r_{0} - \frac{b_{1}}{2}}},{{{where}\mspace{14mu} r_{0}} = {{- \frac{b_{1}}{2}} \cdot \frac{\left( {\frac{v_{2}}{v_{1}} + 1} \right)}{\left( {1 - \frac{v_{2}}{v_{1}}} \right)}}}$

-   -   ascertaining the steering angle α₃ using the relationship

${\alpha_{3} = {{arc}\; {\tan \left( \frac{a_{1}}{r_{1}} \right)}}},$

-   -    where v₁ denotes the velocity of the drivable wheel on the        inside of the curve, v₂ the velocity of the drivable wheel on        the outside of the curve, ψ the yaw rate, α₃ the steering angle        of the steering wheel on the inside of the curve, r₁ the circle        radius of the drivable wheel on the inside of the curve, r₂ the        circle radius of the drivable wheel on the outside of the curve,        a₁ the wheelbase, and b₁ the track width.

This object is further achieved by a device for ascertaining thesteering angle α₃ of at least one wheel of a set of steerable wheels ofa machine that can be directionally controlled, which machine comprisesat least said set of steerable wheels and at least one set of drivablewheels, which wheels have a wheelbase a₁ relative to the steerablewheels and are separated from one another by a specific track width b₁,which device comprises a plurality of wheel velocity sensors forascertaining the respective wheel velocities v₁, v₂ and/or values thatare directly related thereto, for example, the revolution counts n₁, n₂of the drivable wheels, which device also comprises a control deviceadapted to receive the ascertained wheel velocities, and/or the valuesdirectly related thereto, e.g., the revolution counts n₁, n₂ of thedrivable wheels, from which values it ascertains the steering angle α₃of at least one steerable wheel.

For the purposes of the present invention, the term ‘wheel velocitysensors’ is understood as referring to all sensors capable of being usedfor the detection of the velocity of a wheel. Hence, it also includesthose sensors that are adapted to detect a wheel's revolution count orsimilar values from which the wheel's velocity can be ascertained.

Unlike the devices and methods of the prior art for ascertaining thesteering angle of a machine that can be directionally controlled, nosteering angle sensors are used, and more particularly, no such sensorsare disposed on the steerable wheels. Rather, ascertainment of therespective steering angle is performed using a dedicated control device,based on machine-specific data and using suitable velocity sensors,revolution count sensors, and other sensors on the drivable wheels.

In this context, it may again be pointed out that instead of detectingthe wheel velocity of the individual drivable wheels, it is of coursepossible to discern the revolution counts thereof, in order then tocompute the wheel velocity from the known wheel diameter and therevolution count. It may also be pointed out that in addition toascertaining the steering angle α₃ of a wheel on the inside of thecurve, all of the other steering angles of the vehicle can beascertained by way of its known geometries.

An essential advantage of the claimed method or the claimed device ofthe present invention is the increase in reliability achieved, since farfewer mechanical items are necessary for ascertaining the steeringangle. The method of the present invention allows, furthermore, fordirect ascertainment of the real steering angle of the respectivesteering wheel, in which case, in particular, erroneous detections dueto machine-specific inaccuracies are avoided.

In the context of the claimed method or claimed device of the presentinvention, it is possible to differentiate between a wheel on the insideof a curve and that on the outside thereof, whether a steering ordrivable wheel, by way of the detected velocity, that is to say, therevolution count of the wheel. When turning, the velocity of the wheelon the outside of the curve is of course higher than that of the wheelon the inside of the curve. This fact is taken into account whenascertaining the steering angle, so that, for example, when determiningthe wheel velocity difference Δv, unequivocal results will always beachievable.

According to one aspect of the present invention, a velocity signal, ora revolution count signal, is ascertained for each wheel using wheelvelocity sensors on the drivable wheels. The steering angle α₃ can thenbe ascertained from these two signals coming from the two drivablewheels, either through computation of the yaw rate and the real circleradius r₁ of the drivable wheel, or through ascertaining the real circleradius r₁ and the mid-point radius r₀ of the steering angle α₃.

The device of the present invention comprises, furthermore, a controldevice configured such that it can execute the ascertainment of therequired data and can draw conclusions from the vehicle geometries andthe detected velocities or revolution counts, etc.

The sensors of the device of the present invention can, for example, berevolution count sensors as known per se, in connection with anelectronic control unit, or alternatively, in the case of a hydraulicdrive, they can be pressure sensors, used to detect the pressuresgenerated in the respective hydraulic pumps. It is also possible tocompute the wheel velocity of the drivable wheels by way of powersensors, or by measuring filling levels in hydraulic control elements.

In the case of machines in which the steering angle of the steerablewheels is directly coupled to the velocity of the drivable wheels inorder, for example, to ensure precise turning, the method and devicedescribed above are particularly advantage, since the ascertainment ofthe steering angle can be integrated seamlessly into the couplingprocess between the velocity of the driving (rear) wheels and theadjustment of the steering angle of the steerable (front) wheels. Inthis respect, the present invention thus also relates to a machine inwhich the steering angle is ascertained in the aforementioned manner, orto a machine in which a corresponding device for determining thesteering angle is provided, and in which there is direct feedbackbetween the steering angle and the propulsion velocity of the drivablewheels, to ensure driving along an optimal curve, particularly a curvewithout the occurrence of wheel slip.

In order to ascertain exact steering angles even when a wheel slips, andto avoid measurement inaccuracy of the steering angle due to slipping ofat least one drivable wheel, slip detection is preferably carried out.An appropriate slip indicator is used depending on whether or not atleast one of the drivable wheels is slipping. When the slip indicatorshows positive results, the (previously) found value for the steeringangle is preferably retained during steering angle detection. If, in thecase of positive slip indication, i.e., if a wheel is slipping, thevalue for the steering angle is changed in accordance with experiencedvalues, there would be the risk that the change in velocity accompanyinga slip of the front wheel might lead to inaccurate ascertainment of asteering angle. Alternatively, it might falsely be interpreted as beingan adjustment in the steering angle, or as being an entirely newsteering angle.

For slip detection in the above context, it is possible to perform aplausibility check on the detected wheel velocities or the detectedrevolution count of at least one of the drivable wheels. There arevarious ways of doing this.

In particular, it is possible, during the plausibility check, toascertain the progression of the wheel velocity and/or the progressionof the rotational speed and/or the progression of values directlyrelated to these values, and to compare these with a progressionthreshold value, where a positive slip indicator is set when thisthreshold is underrun or overrun.

The progression threshold value can, for example, be a minimum permittedperiod t_(min) of all detected changes in wheel velocity over a timeperiod t. A suitable time period is, for example, 0.5 second≦t_(m)≦2seconds, or more particularly, t_(min)=1 second. That is to say, a sliphas happened or is assumed to have happened when the velocity of atleast one wheel, or the wheel velocity difference between the twowheels, changes from a starting value to an end value over a time periodt<t_(min), which time period is very short, e.g., less than one second.This is significant when the change in velocity, or the change in thewheel velocity difference, is detected at time t=0 and has finishedbefore the minimum permitted period t_(min) has elapsed and the velocityhas assumed a new value. The above also holds, identically, for therevolution count, or a change in revolution count of the wheels.

It is also possible for a progression threshold value to describe amaximum permitted change in wheel velocity and/or rotational speedwithin the plausibility time period, in particular, a maximum permittedchange of from 10% to 30%, and, more particularly, one of 20%. In thiscase, the progression threshold value is taken as the maximum permittedchange in wheel velocity and/or in the wheel velocity difference, and anoverrun of the progression threshold value occurs when, for example, thewheel velocity suddenly changes, particularly when it undergoes a changeof 10% to 30% within a given time period t, more particularly, when itundergoes a change of 20% in that time period. Here again, the change isto be understood as that occurring over the whole time period from thebeginning of the change to its end. The above holds, identically, forthe revolution counts of the wheels.

It is further possible to set the threshold progression value such thatit applies when a detected change in wheel velocity of one wheel isapproximately 0% and a detected change in wheel velocity of the otherwheel is greater than 0%. If it is found that one wheel has undergone achange in velocity while the other has undergone no such change, wheelslipping can be inferred. If the threshold progression value is setaccording to these conditions, the plausibility check can compare thedetected wheel velocities, etc., with the configured thresholdprogression value and set a positive slip indicator as necessary. Hereagain, changes of the revolution count of the wheels can be detected andassessed accordingly.

A threshold progression value can further be set such that it applieswhen a detected change in wheel velocity v₁ or v₂, or a change inrevolution count, is approximately zero and a detected change in theother wheel velocity v₂ or v₁ respectively, or a change of revolutioncount, is greater than zero. This arrangement also allows for detectionof slipping.

Of course, the methods described above for slip detection can be appliedsingly or in combination with one another.

The control device preferably comprises a slip detecting device toperform slip detection, which is configured such that it carries out theplausibility check based on the detected velocities or revolution countsof the drivable wheels, in order to exclude inaccuracy in theascertainment of the steering angle due to the presence of slipping ofat least one of the drivable wheels.

This slip detecting device makes it possible, in particular, to recordthe progression of the wheel velocity and/or the progression of thedifference in wheel velocities and/or the progression of values directlyrelated to these values, such as, for example, progression in revolutioncount, progression in time, acceleration or deceleration, driving power,the time period of changes, etc.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention is described below with reference to an exemplaryembodiment illustrated in the drawings, in which:

FIG. 1 is a diagrammatic side view of a self-propelled constructionmachine, in particular, a paving machine;

FIG. 2 is a diagrammatic plan view of an embodiment of a machine thatcan be directionally controlled, including geometric machine data;

FIG. 3 shows the embodiment illustrated in FIG. 2, including anembodiment of the device of the invention for ascertaining the steeringangle of a steerable wheel;

FIG. 4 is a flow chart for carrying out an embodiment of the method ofthe invention for ascertaining the steering angle of at least onesteerable wheel of a machine as illustrated in FIG. 2;

FIG. 5 is a steering schema demonstrating a steering operation of theexemplary embodiment illustrated in FIG. 2; and

FIG. 6 is a steering schema for an exemplary embodiment illustrated inFIG. 2 on the occurrence of slip.

DETAILED DESCRIPTION OF THE INVENTION

A self-propelled construction machine, designed as a road paver 10,comprises, according to FIGS. 1 and 2, a chassis with three pairs ofwheels, of which only the left-hand wheels 1, 2, and 5 are visible inFIG. 1. The full complement of wheels is visible in FIG. 2. The wheels1, 2 of a first wheel pair are designed as drivable wheels. Two furtherpairs 12, 14 are disposed on a tandem bogie, and are respectivelyequipped with steerable wheels 3, 4 and 5, 6. This machine thus has adoubly steerable front axle or tandem axle. The forward direction oftravel is designated by V.

In the following description, identical or identically functioning partsare designated by the same reference signs, with occasional subscriptnumerals for disambiguation.

FIG. 2 shows a plan view of the chassis of the paving machine 10 whentraveling along a curve, more particularly, when turning to the left.

The drivable wheels 1, 2 are disposed on a common axle, separated fromeach other by the track width b₁. The drivable wheels 1, 2 arefurthermore separated from the set 12 of steerable wheels 3, 4 by thewheelbase a₁. This machine is geometrically constructed such that theindividual wheels 1, 2 are again separated by a wheelbase a₁ from thewheels 3 and 4, respectively.

In FIG. 2, all of the steerable wheels 3, 4, 5, 6 are turned, and it isthus visible that each wheel has a distinct Ackermann angle inaccordance with its axle-pivot steering system. The Ackermann (orsteering) angle of the wheel 3 on the inside of the curve is designatedhere by the reference sign α₃. With forward movement in the direction ofthe arrow V (FIG. 1) by means of the drivable wheels 1, 2, the machine10 turns as defined by the radius r₃ referring to the wheel 3, due tothe steering action of the steerable wheels 3, 4, 5, 6.

As shown in FIG. 3, the machine 10 has a control device 8, by means ofwhich the driving power of the drivable wheels 1, 2 and the steeringaction of the steerable wheels 3, 4, 5, 6 can be controlled. Wheelvelocity sensors 21, 22 are disposed on the drivable wheels 1, 2 forascertaining relevant control data, which sensors are adapted to detectthe individual wheel velocities v₁, v₂, or the revolution counts n₁, n₂,of the drivable wheels 1 and 2, respectively. The driving power itselfcan come, for example, from hydraulic motors 31, 32, allocated to theindividual drivable wheels 1, 2, providing independent driving power forthe respective wheels. Direct access to the driving motors 31, 32 bymeans of the control device 8 is possible.

The control device 8 comprises, inter alia, a slip detecting device 9,by means of which detection of the occurrence of slip of at least one ofthe drivable wheels 1, 2 is possible, as described in detail below. Moreparticularly, a plausibility check of the detected wheel velocity v₁, v₂of the drivable wheels 1, 2 or of values directly related thereto ispossible.

As shown in FIG. 4 in conjunction with FIG. 2 and FIG. 3, ascertainingthe steering angle α₃ takes place in the following manner:

Vehicle data pertaining to the machine 10 and relevant to ascertainmentof the steering angle α₃ are stored in the control device 8, or in adevice associated therewith. Such data can be, for example, the trackwidth b₁, the circumference or radius of the wheels 1, 2 and thewheelbase a₁ between the drivable wheels 1 and 2 and the set 12 ofsteerable wheels 3, 4.

While operating, whether traveling to, or working at, a site, therevolution count or the wheel velocity of the drivable wheels 1, 2 isdetected by way of the wheel velocity sensors 21, 22, which sensors arelinked to the control device 8. As mentioned above, the wheel velocitysensors may determine the velocity of the drivable wheels 1, 2 directly,or they may ascertain the wheel revolution count, that is, its rotationvelocity, from which the wheel velocity can be computed. FIG. 4demonstrates such a procedure.

The velocity v₁, v₂ of the two drivable wheels 1, 2 is here ascertainedby way of the wheel turning velocity n₁, n₂ as ascertained through thewheel velocity sensors 21, 22 and the known circumference U of thewheels 1, 2, in combination with the vehicle data stored in the controldevice 8.

By means of this velocity, the yaw rate P can be ascertained, as can thecircle radius r₁ of the wheel on the inside of the curve, and the circleradius r₀ of the mid-point of the distance between the inner wheel andthe outer wheel.

Taking into account the radius r₁ of the wheel 1 on the inside of thecurve, the following relationships hold:

v₁ = r₁ψ v₂ = (r₁ + b₁)ψ$\psi = {\left. \frac{v_{2} - v_{1}}{b_{1}}\rightarrow r_{1} \right. = \frac{v_{1}}{\psi}}$$\alpha_{3} = {{arc}\; {\tan \left( \frac{a_{1}}{r_{1}} \right)}}$

To calculate the circle radius r₀ of the middle of the vehicle, alongwhich circle the mid-point of the distance between the inner wheel andthe outer wheel moves, the following relationships should be used:

$\frac{r_{1}}{r_{2}} = \frac{n_{2}}{n_{1}}$$\frac{r_{0} + \frac{b_{1}}{2}}{r_{0} - \frac{b_{1}}{2}} = \frac{n_{2}}{n_{1}}$$r_{0} = {{{- \frac{b_{1}}{2}} \cdot \frac{\left( {\frac{n_{2}}{n_{1}} + 1} \right)}{\left( {1 - \frac{n_{2}}{n_{1}}} \right)}} = \frac{a_{1}}{\tan \; \alpha_{3}}}$$\alpha_{3} = {\arctan \left( {{- \frac{2a_{1}}{b_{1}}} \cdot \frac{\left( {1 - \frac{n_{2}}{n_{1}}} \right)}{\left( {\frac{n_{2}}{n_{1}} + 1} \right)}} \right)}$

where:

v₁ denotes the velocity of the drivable wheel on the inside of thecurve;

v₂ denotes the velocity of the drivable wheel on the outside of thecurve;

n₁ denotes the revolution count of the drivable wheel on the inside ofthe curve;

n₂ denotes the revolution count of the drivable wheel on the outside ofthe curve;

ψ denotes the yaw rate;

α₃ denotes the steering angle of the steerable wheel on the inside ofthe curve;

r₁ denotes the circle radius of the drivable wheel on the inside of thecurve;

r₂ denotes the circle radius of the drivable wheel on the outside of thecurve;

a₁ denotes the wheelbase;

b₁ denotes the track width.

As shown in FIG. 2, the ascertained circle radius r₁ of the drivablewheel 1 on the inside of the curve is directly related to the steeringangle α₃ and the wheelbase a₁, such that the steering angle α₃ can beascertained as follows:

$\alpha_{3} = {{arc}\; {\tan \left( \frac{a_{1}}{r_{1}} \right)}}$

As an alternative to this approach, the steering angle α₃ can beascertained using the geometrical relationships between the inner andouter circle radii r₁, r₂ of the inner and outer drivable wheels r₁, r₂.In such a case, the steering angle α₃ is obtained from the followingequations:

$\frac{r_{1}}{r_{2}} = \frac{v_{2}}{v_{1}}$$\frac{r_{0} + \frac{b_{1}}{2}}{r_{0} - \frac{b_{1}}{2}} = \frac{n_{2}}{n_{1}}$$r_{0} = {{{{- \frac{b_{1}}{2}} \cdot \frac{\left( {\frac{n_{2}}{n_{1}} + 1} \right)}{\left( {1 - \frac{n_{2}}{n_{1}}} \right)}}:r_{1}} = {r_{0} - \frac{b_{1}}{2}}}$

where:

v₁ denotes the velocity of the drivable wheel on the inside of thecurve;

v₂ denotes the velocity of the drivable wheel on the outside of thecurve;

n₁ denotes the revolution count of the drivable wheel on the inside ofthe curve;

n₂ denotes the revolution count of the drivable wheel on the outside ofthe curve;

ψ denotes the yaw rate;

α₃ denotes the steering angle of the steerable wheel 3 on the inside ofthe curve;

r₁ denotes the circle radius of the drivable wheel 1 on the inside ofthe curve;

r₂ denotes the circle radius of the drivable wheel 2 on the outside ofthe curve;

a₁ denotes the wheelbase;

b₁ denotes the track width.

The steering angle α₃ is again determined as follows:

$\alpha_{3} = {{arc}\; {\tan \left( \frac{a_{1}}{r_{1}} \right)}}$

Provided that neither of the drivable wheels 1, 2 is slipping, the exactsteering angle α₃ of the machine 10 will be obtained in a very simplemanner.

The effect of the steering operation on the velocity v₁, v₂ of thedrivable wheels 1, 2, or respectively, on the revolution count n₁ ofwheel 1, and the revolution count n₂ of wheel 2, is demonstrated in FIG.5.

While the machine is moving directly forward, that is, when there is nosteering input a acting on the steerable wheels 3, 4, 5, 6, the drivablewheels 1, 2 move synchronously. The revolution count n₁, n₂ of the twowheels is identical. As soon as steering input from a suitableregulating device starts, the revolution counts n₁, n₂ of the two wheels1, 2 change in a geometrically dependent fashion, in which case thewheel 1 on the inside of the curve undergoes a reduction in revolutioncount −Δn₁, and the wheel 2 on the outside of the curve undergoes anincrease in revolution count +Δn₂. The same holds for the respectivechanges in velocity Δv.

In the example shown, there is initially steering input to the left,which lasts for a first steering period t₁. This steering period t₁ isgoverned by the steering angle α. The larger the steering angle α, theshorter the steering period t₁. During the steering operation, the wheel1 on the inside of the curve rotates with a revolution count n₁, whichis lower than the revolution count n₂ of the wheel 2 on the outside ofthe curve. In the example shown, the revolution count n₁ of the wheel 1on the inside of the curve for steering period t₁ decreases withincreasing steering angle α, while the revolution count n₂ of the wheel2 on the outside of the curve increases by the same amount. At the endof a steering period t₁ the absolute value of the reduction inrevolution count −Δn₁ of the wheel 1 on the inside of the curve is equalto that of the increase in revolution count +Δn₂ of the wheel 2 on theoutside of the curve. The gradient β₁ shown in FIG. 5, of theprogression of the revolution count of the wheel 1 on the inside of thecurve thus corresponds, with opposite sign, to the gradient β₂ of theprogression of the revolution count of the wheel 2 on the outside of thecurve.

This operation is repeated with inverted signs when there is steeringinput for a negative steering angle −α for a further steering period t₂in the opposite direction, that is to say, to the right.

In FIG. 5, two further steering operations are shown by way of example,these being carried out for a third steering period t₃ and a fourthsteering period t₄, which are shorter than the first and second steeringperiods t₁ and t₂, so that there result a smaller increase in revolutioncount +Δn₁′ and a smaller decrease in revolution count +Δn₂′.

If the changes in revolution count Δn₁, Δn₁′ of the wheel 1 on theinside of the curve and the changes in revolution count Δn₂, Δn₂′ of thewheel 2 on the outside of the curve are of equal magnitude for a givensteering input, the associated steering angle α can be derivedtherefrom, and consequently the steering input for the steerable wheels3, 4, 5, 6 can be inferred.

Furthermore, it is possible to ascertain, by way of the revolutioncounts n₁ and n₂ or n₃ and n₄ of the two wheels 1, 2, respectively, andtheir respective revolution count changes Δn₁, Δn₂ or Δn₁′, Δn₂′,whether one of the two wheels 1, 2 is slipping. If, as in the exampleillustrated in FIG. 5, the revolution count changes Δn₁, Δn₂ or Δn₁′,Δn₂′, of the two wheels 1, 2 are equal in magnitude within each pair, noslip is occurring. If, with the same steering angle α, their magnitudesdiffer within the pair, slipping is taking place.

In the same way, the gradients β₁, β₂, β₁′, β₂′ of the revolution countprogressions of the wheel 1 on the inside of the curve and those of thewheel 2 on the outside of the curve, can make it possible to determinewhether there is slipping between the two wheels 1, 2. If, according toFIG. 5, the gradients β₁, β₂ or β₁′, β₂′ are equal in magnitude for eachpair, no slipping is taking place. A deviation of the gradients β₁, β₂or β₁′, β₂′ from each other indicates that slipping is occurring.

For practical applications it is appropriate to designate a maximumpermitted change in revolution count ±Δn_(max) for a steering operation,which is valid for both wheels 1, 2 and which is typical of a steeringoperation. In the examples illustrated in FIG. 5 this maximum permittedchange in revolution count is not exceeded for any steering operation.If this maximum change in revolution count ±Δn_(max) is exceeded, thissignifies that the relevant wheels 1, 2 are spinning. A typical exampleaccording to FIG. 5 is a maximum permitted change in revolution count of±Δn_(max) of 20%.

The maximum permitted change in revolution count ±Δn_(max) represents amaximum gradient. All of the gradients β₁, β₂ or β₁′, β₂′ of theexemplary embodiment illustrated in FIG. 5 are accordingly below themaximum gradient.

FIG. 6 is a diagrammatical representation of the state when the machine10 is moving forwards, in a situation where there is slipping of thedrivable wheels 1, 2. Despite the fact that the machine 10 is movingdirectly forwards, and the steering angle α is thus 0°, the wheelvelocity sensors 21, 22 (FIG. 3) on the wheels 1, 2 will detect, in arelatively short first time period t₁S, a wheel velocity change or afirst reduction in revolution count −Δn₁S of the wheel 1 on the insideof the curve and an increase in revolution count +Δn₂S of the wheel 2 onthe outside of the curve. The increase in revolution count +Δn₂S and thereduction in revolution count −Δn₁S are respectively above and below themaximum permitted change in revolution count ±Δn_(max). That is to say,both wheels are spinning. In the same way the gradients βS₁, βS₂ aresteeper than the maximum permitted gradient, from which it can also beconcluded that slipping is present.

In a relatively short second time period t₂S it is detected that thereis a reduction in revolution count −Δn₂S′ of the wheel 2 on the outsideof the curve and an increase in revolution count +Δn₁S′ of the wheel 1on the inside of the curve, as measured from the starting value forrevolution count, where the associated gradients are again greater thanthe maximum permitted gradient. Slipping is thus also present in thiscase.

With the revolution count changes +Δn₂S′, −Δn₁S′, which take placeduring a third t₃S time period and a fourth t₄S time periodrespectively, and which are less than the maximum permitted change inrevolution count ±Δnmax, the example illustrated in FIG. 6 has gradientsthat are larger than the maximum permitted gradient. Hence, slipping isalso occurring in this case, despite the fact that the permitted maximumchanges in revolution count ±Δnmax have not been exceeded.

A slip of the wheels 1, 2 can also be ascertained from the circumstancethat the time in which a given revolution count has been achieved isshorter than the time that would be necessary to achieve the samerevolution count with a usual steering operation. As FIG. 6 shows whencompared with FIG. 5, the first time period t₁S, in which the change inrevolution count Δn₁′ takes place, is shorter than a minimum permittedtime period tL_(min), which may not be undershot in order to allow thepermitted maximum revolution count ±Δn_(max) to be reached (t₁S<tL_(min)).

In such cases a positive slip indicator can be set in the control device8. In this case, when ascertaining the steering angle α, no change willbe made to the previously detected steering angle α.

According to the present invention, in the embodiment illustrated, aplausibility check of the detected velocities v₁, v₂ or measured valuesrelated thereto is always carried out for slip detection. Moreparticularly, this plausibility check involves ascertaining theprogression of the wheel velocities v₁, v₂ and/or the progression of thewheel velocity difference Δv and/or the progression of measured valuesdirectly related to these values, and comparing these values with athreshold value as described above, in which case if one of thethreshold values is overrun or underrun a positive slip indicator isset.

Such a progression threshold value can thus, for example, be the minimumpermitted time period tL_(min) in which all of the detected wheelvelocity changes or revolution count changes Δn take place. For example,in the embodiment as illustrated in FIG. 6, the minimum permitted timeperiod tL_(min) is set to be 1 second. When revolution count changes Δnthat take place entirely within the permitted minimum time periodtL_(min) are detected, slipping can be inferred and the slip indicatorcan be set as positive.

To guarantee that the steering angle is ascertained without error, aslip detection procedure is carried out, according to the invention,during the process of ascertaining the steering angle, and the value forthe detected steering angle is only then corrected if no positive slipindicator has been set.

1. A method for ascertaining a steering angle (α₃) of at least onesteerable wheel of a set of steerable wheels of a machine that can bedirectionally controlled, which machine comprises at least said set ofsteerable wheels and at least one set of drivable wheels having aspecific wheelbase (a₁) relative to said steerable wheels and spacedfrom one another by a track width (b₁), comprising: detecting a wheelvelocity of the at least two drivable wheels; ascertaining a wheelvelocity difference (Δv) between velocities (v₁; v₂) of said twodrivable wheels; ascertaining a yaw rate (ψ) using the relations$\psi = \frac{v_{2} - v_{1}}{b_{1}}$ ascertaining a real circle radius(r₁) of the drivable wheel on an inside of a curve using therelationship $r_{1} = \frac{v_{1}}{\psi}$ ascertaining the steeringangle α₃ using the relationship${\alpha_{3} = {{arc}\; {\tan \left( \frac{a_{1}}{r_{1}} \right)}}},$ in which: v₁ denotes the velocity of the drivable wheel on the insideof the curve, v₂ denotes the velocity of the drivable wheel on anoutside of the curve, ψ denotes the yaw rate, α₃ denotes the steeringangle of the steerable wheel on the inside of the curve, r₁ denotes thecircle radius of the drivable wheel on the inside of the curve, r₂denotes a circle radius of the drivable wheel on the outside of thecurve, a₁ denotes the wheelbase, and b₁ denotes the track width.
 2. Amethod for ascertaining a steering angle (α₃) of at least one steerablewheel of a set of steerable wheels of a machine that can bedirectionally controlled, which machine (10) comprises at least said setof steerable wheels and at least one set of drivable wheels having aspecific wheelbase (a₁) relative to said steerable wheels and spacedfrom one another by a track width (b₁), comprising: detecting a wheelvelocity (v₁; v₂), or a measured value directly related thereto, such asthe revolution count (n₁; n₂), of the at least two drivable wheels;ascertaining a real circle radius (r₁) of the driven wheel (1) on aninside of a curve using the relationship${r_{1} = {r_{0} - \frac{b_{1}}{2}}},{{{{where}\mspace{14mu} r_{0}} = {{- \frac{b_{1}}{2}} \cdot \frac{\left( {\frac{v_{2}}{v_{1}} + 1} \right)}{\left( {1 - \frac{v_{2}}{v_{1}}} \right)}}};}$ascertaining a steering angle α₃ using the relationship${\alpha_{3} = {{arc}\; {\tan \left( \frac{a_{1}}{r_{1}} \right)}}},$ where: v₁ denotes the velocity of the driven wheel on the inside of thecurve, v₂ denotes the velocity of the driven wheel on an outside of thecurve, ψ denotes a yaw rate, α₃ denotes the steering angle of thesteerable wheel on the inside of the curve, r₁ denotes the circle radiusof the driven wheel on the inside of the curve, r₂ denotes a circleradius of the driven wheel on the outside of the curve, a₁ denotes thewheelbase, and b₁ denotes the track width.
 3. The method according toclaim 1, wherein slip detection is carried out in order to excludeerroneous ascertainment of the steering angle (α₃) due to the presenceof slip on at least one of the drivable wheels.
 4. The method accordingto claim 3, wherein said slip detection involves a plausibility check ofthe detected wheel velocity (v₁; v₂) of at least one of the drivablewheels.
 5. The method according to claim 4, wherein said plausibilitycheck involves ascertaining the progression of the wheel velocities v₁,v₂ of at least one wheel and/or the progression of the wheel velocitydifference (Δv) of the two wheels and/or the progression of measuredvalues directly related to these values, and comparing these values witha progression threshold value, in which case if one of the thresholdvalues is overrun or underrun a positive slip indicator is set.
 6. Themethod according to claim 4, wherein the progression threshold value isthe maximum permitted change in wheel velocity (v₁; v₂) and/or change inthe wheel velocity difference (Δv) during a plausibility time period,and is a maximum permitted change ranging from 10% to 30%.
 7. The methodaccording to claim 4, wherein the progression threshold value is achange in wheel velocity of one wheel of approximately 0% while adetected change in wheel velocity of the other wheel is greater than 0%.8. The method according to claim 5, wherein in the case of a setpositive slip indicator, the previously ascertained or set value of thesteering angle (α) is retained.
 9. A device for ascertaining a steeringangle (α₃) of at least one steerable wheel of a set of steerable wheelsof a machine that can be directionally controlled, which machinecomprises at least said set of steerable wheels and at least one set ofdrivable wheels having a specific wheelbase (a₁) relative to saidsteerable wheels and spaced from one another by a track width (b₁), saiddevice comprising: a plurality of wheel velocity sensors for detectingrespective wheel velocities (v₁, v₂) of said drivable wheels, and acontrol device adapted to receive the detected wheel velocities (v₁, v₂)of said driven wheels, from which the control device ascertains thesteering angle (α₃) of at least one steerable wheel using at least oneof the following relationships:${\alpha_{3} = {{arc}\; {\tan \left( \frac{a_{1}}{r_{1}} \right)}}},{{{where}\mspace{14mu} \psi} = \frac{v_{2} - v_{1}}{b_{1}}},{{r_{1} = \frac{v_{1}}{\psi}};{or}}$${r_{1} = {r_{0} - \frac{b_{1}}{2}}},{{{where}\mspace{14mu} r_{0}} = {{{- \frac{b_{1}}{2}} \cdot \frac{\left( {\frac{v_{2}}{v_{1}} + 1} \right)}{\left( {1 - \frac{v_{2}}{v_{1}}} \right)}}\mspace{14mu} {or}}}$${r_{0} = {{{- \frac{b_{1}}{2}} \cdot \frac{\left( {\frac{n_{2}}{n_{1}} + 1} \right)}{\left( {1 - \frac{n_{2}}{n_{1}}} \right)}}:}},$ respectively, where v₁ denotes the velocity of the drivable wheel onthe inside of a curve; v₂ denotes the velocity of the drivable wheel onan outside of the curve; ψ denotes a yaw rate; α₃ denotes the steeringangle of the steerable wheel on the inside of the curve r₁ denotes acircle radius of the drivable wheel on the inside of the curve; r₂denotes a circle radius of the drivable wheel on the outside of thecurve; r₀ denotes a circle radius of the midpoint of the track widthbetween the drivable wheels on the inside and outside of the curve; a₁denotes the wheelbase; and b₁ denotes the track width.
 10. The deviceaccording to claim 9, wherein said control device comprises a slipdetecting device which is configured such that a plausibility check ofthe detected wheel velocities (v₁; v₂) of said driven wheels can becarried out in order to avoid erroneous ascertainment of said steeringangle (α₃) due to slipping of at least one of the driven wheels.
 11. Themethod according to claim 2, wherein slip detection is carried out inorder to exclude erroneous ascertainment of the steering angle (α₃) dueto the presence of slip on at least one of the drivable wheels.
 12. Themethod according to claim 11, wherein said slip detection involves aplausibility check of the detected wheel velocity (v₁; v₂) of at leastone of the drivable wheels.
 13. The method according to claim 12,wherein said plausibility check involves ascertaining the progression ofthe wheel velocities v₁, v₂ of at least one wheel and/or the progressionof the wheel velocity difference (Δv) of the two wheels and/or theprogression of measured values directly related to these values, andcomparing these values with a progression threshold value, in which caseif one of the threshold values is overrun or underrun a positive slipindicator is set.
 14. The method according to claim 12, wherein theprogression threshold value is the maximum permitted change in wheelvelocity (v₁; v₂) and/or change in the wheel velocity difference (Δv)during a plausibility time period, and is a maximum permitted changeranging from 10% to 30%.
 15. The method according to claim 12, whereinthe progression threshold value is a change in wheel velocity of onewheel of approximately 0% while a detected change in wheel velocity ofthe other wheel is greater than 0%.
 16. The method according to claim13, wherein in the case of a set positive slip indicator, the previouslyascertained or set value of the steering angle (α) is retained.